Magnetism in Simple Metal and 4<Emphasis Type="Italic">d</Emphasis> Transition Metal Clusters

In this review article I discuss two aspects of magnetism in small metal clusters. The first question discussed is whether simple metal clusters, that obey electronic shell models and mimic properties of elemental atoms, also obey Hund’s rule of maximum spin multiplicity. The second question is whether small clusters of 4d transition metal atoms, that are non-magnetic in the bulk, have magnetic ground states. The question arises because calculations showed that small V clusters are magnetic although the bulk metal is not. We discuss known results on Rh clusters in detail to show that small clusters are generally magnetic, but it is difficult to unequivocally identify the ground state due to the presence of many isomers and spin states that are very close in energy.     

Shell effects in planar electron clusters

We investigate the electronic shell structure of planar metal clusters, having in mind clusters on insulating surfaces with an interface energy such that the cluster covers the surface in a monolayer. In this first survey we concentrate on the shell effects of such a planar electron cloud using the Ultimate Jellium Model where the structural effects of the positive background are completely eliminated. An axially symmetric electron cloud shows shell effects which are, however, somewhat smaller than those of fully free threedimensional clusters. The free variation of the shape for planar clusters on surfaces, leading to many triaxial clusters, diminishes the shell effects even further, leading to the existence of hybrid-deformed clusters and a lack of energetically favored “magic” clusters in an intermediate size range N ≈ 10.30. In contrary to the situation for free clusters the small shell energies have a minor effect on the energetics of the groundstate. As a consequence, electronic shell effects are only one ingredient amongst others to determine the kinetics of cluster growth on (insulating) substrates. With a bold rescaling assumption, we can relate axially symmetric planar clusters to the planar electron cloud in a neutral quantum dot, having the consequence that shell effects persist to play a role in these systems.     

Semiclassical description of large multipole-deformed metal clusters

We use the semiclassical periodic orbit theory to describe large metal clusters with axial quadrupole, octupole, or hexadecapole deformations. The clusters are regarded as cavities with ideally reflecting walls. We start from the case of spherical symmetry and then apply a perturbative approach for calculating the oscillating part of the level density in the deformed case. The advantage of this approach is that one only has to know the periodic orbits of the spherical cavity, which makes the calculation very simple. This perturbative method is a priori restricted to small deformations. However, the results agree quite well with those of quantum-mechanical calculations for deformations that are not too large, such as typically occur for the ground states of metal clusters. We also calculate shell-correction energies. With this, it becomes possible to predict at least qualitatively the deformation energy of metal clusters.     

Theory for the atomic shell structure of the cluster magnetic moment and magnetoresistance of a cluster ensemble

We present a simple theory for the cluster size dependence of the average cluster magnetic moment of transition metal clusters. Assuming a local environmental dependence of the atomic magnetic moments, the cluster magnetization exhibits a magnetic shell structure, reflecting the atomic structure of the cluster. Thus, the observed oscillations of the average cluster magnet moment may serve as a fingerprint of the cluster geometry. We also discuss the giant magnetoresistance (GMR) exhibited by an ensemble of magnetic clusters embedded in a metallic matrix. It is shown that the magnetic anisotropy affects strongly the magnetization of the cluster ensemble under certain conditions. Since the GMR depends on the cluster ensemble magnetization, it can be used to determine the cluster magnetic anisotropy energy.     

Restricted and unrestricted Hartree–Fock approaches applied to spherical quantum dots in a magnetic field

The Roothaan and Pople–Nesbet approaches for real atoms are adapted to quantum dots in the presence of a magnetic field. Single‐particle Gaussian basis sets are constructed, for each dot radius, under the condition of maximum overlap with the exact functions. The chemical potential, charging energy, and total spin expected values are calculated, and we have verified the validity of the quantum dot energy shell structure as well as Hund's rule for electronic occupation at zero magnetic field. At finite field, we have observed the violation of Hund's rule and studied the influence of magnetic field on the closed and open energy shell configurations. We have also compared the present results with those obtained within the LS‐coupling scheme for low electronic occupation numbers. We focus only on ground‐state properties and consider quantum dots populated up to 40 electrons, constructed by GaAs or InSb nanocrystals. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Fluorescence quenching near small metal nanoparticles

We develop a microscopic model for fluorescence of a molecule (or semiconductor quantum dot) near a small metal nanoparticle. When a molecule is situated close to metal surface, its fluorescence is quenched due to energy transfer to the metal. We perform quantum-mechanical calculations of energy transfer rates for nanometer-sized Au nanoparticles and find that nonlocal and quantum-size effects significantly enhance dissipation in metal as compared to those predicted by semiclassical electromagnetic models. However, the dependence of transfer rates on molecule's distance to metal nanoparticle surface, d, is significantly weaker than the d(-4) behavior for flat metal surface with a sharp boundary predicted by previous calculations within random phase approximation.     

Perspectives on double-excitations in TDDFT

The adiabatic approximation in time-dependent density functional theory (TDDFT) yields reliable excitation spectra with great efficiency in many cases, but fundamentally fails for states of double-excitation character. We discuss how double-excitations are at the root of some of the most challenging problems for TDDFT today. We then present new results for (i) the calculation of autoionizing resonances in the helium atom, (ii) understanding the nature of the double excitations appearing in the quadratic response function, and (iii) retrieving double-excitations through a real-time semiclassical approach to correlation in a model quantum dot.     

Colloidal CdSe quantum dot electroluminescence: ligands and light-emitting diodes

We examine the effects of surface ligand exchange on the performance of hybrid organic/inorganic light emitting diodes (LEDs) that use colloidal nanocrystal quantum dots as emissive centers. Using a series of primary alkylamines with different alkane chain lengths, we exchange the native surface ligands on a series of CdSe/CdZnS/ZnS core/shell/shell nanocrystal quantum dots and compare the differences in photoluminescence and electroluminescence efficiency of the emissive quantum dot layer. We fabricate LEDs made with octadecylamine-, octylamine-, and butylamine-exchanged quantum dots. We find that the differences in electroluminescence efficiency of the devices are not always proportional to the photoluminescence quantum efficiency of the quantum dots. We discuss this trend both in terms of the competing needs of high photoluminescence efficiency and good charge injection and energy transfer, and also in terms of the different processability and film morphology arising from the use of nanoparticles passivated with shorter ligands. Correspondence: David S. Ginger, Department of Chemistry, University of Washington, Seattle, Washington 98195-1700, USA     

Shells and supershells in metal clusters

Concept of energy shells in finite bound quantum systems and their semi-classical interpretation are reviewed. Level densities are associated with classical periodic orbits of a particle in the mean-field. Orbits responsible for the bunching of levels, or the shells, are those with short trajectory length. The inverse of the trajectory length determines the energy spacing of the shells. When two short orbits have almost equal but slightly different lengths, the corresponding quantum level density shows a global beating pattern enveloping individual shell oscillations. This pattern is called “supershell” and may be observed in metal clusters with more than a thousand valence electrons.     

Simplified semiclassical theory for the electronic shell structure of metallic clusters

We present a simplified theory for the electronic shell structure of large metallic clusters by extending the semiclassical analysis by Gutzwiller, Balian and Bloch. Thus analytical results are given for the shell effect in the Fermi energy and cohesive energy. In particular, results for the temperature dependence of the shell structure are given. New results are presented for the shell structure in the ionization potential and photoyield and for the existence of electronic- versus atomic shell structure as a function of cluster size and temperature. We obtain good quantitative agreement with previous numerical calculations and with experiments on Na clusters.     

原子簇FenB2(n=1～6)结构和性质的DFT研究

本文对上百个Fe_nB₂和Fe_n(n=1～6)原子簇模型进行密度泛函理论计算，用来模拟非晶态合金Fe-B体系的局域结构，并考察类金属元素硼的引入对体系性质的影响。将优化构型的键长和电荷分布与实验数值进行比较，发现本文所使用的原子簇模型在一定程度上可以真实、准确地反映非晶态合金Fe-B体系的局域结构。利用这些构型，我们对其键级、电子、催化以及磁学性质进行了讨论。结果表明：原子簇中均存在着强烈的Fe-B键作用，其中在高铁含量原子簇中Fe-Fe键的作用也较为明显；综合热力学、费米能级及态密度的研究结果，发现原子簇Fe₄B₂在合成氨和固氮过程中有可能表现出更为优越的催化活性。结合对原子簇Fe_n和Fe_nB₂(n=1～6)平均3d轨道布居数的分析，发现原子簇Fe_nB₂(n=1～6)的平均磁矩均小于相应原子簇Fe_n(n=1～6)的理论数值和纯金属铁的实验数值(5.7～6.0 BM)，也就是说原子簇Fe_nB₂(n=1～6)均表现出软磁性。     

Theoretical characterization of triangular CdS nanocrystals: a tight-binding approach

We provide theoretical modeling of the optical spectrum of recently synthesized triangular CdS nanocrystals by means of atomistic tight-binding theory. Both zinc blende and wurtzite structures are considered. Optical properties predicted for triangular prisms are very different from the ones obtained for tetrahedral quantum dots when z-polarized light is employed. In particular, the ground transition is dim for triangular prisms, whereas it is bright and highly intense for tetrahedra. The high sensitivity of the fine optical properties on the quantum dot shape allows us to discriminate between truncated tetrahedra and triangular prisms and also to estimate the thickness of the nanocrystals.     

Chemical bonding in group III nitrides

We analyze in this article the evolution of the chemical bonding in group III nitrides (MN, M = Al, Ga, In), from the N-N bond dominated small clusters to the M-N bond dominated crystals, with the aim of explaining how the strong multiple bond of N(2) is destabilized with the increase in coordination. The picture that emerges is that of a partially ionic bond in the solid state, which is also present in all the clusters. The covalent N-N bond, however, shows a gradual decrease of its strength due to the charge transfer from the metal atoms. Overall, Al clusters are more ionic than Ga and In clusters, and thus the N-N bond is weakest in them. The nitrogen atom charge is seen to be proportional to the metal coordination, being thus a bond-related property, and dependent on the M-N distance. This explains the behavior observed in previous investigations, and can be used as a guide in predicting the structures and defects on semiconductor quantum dot or thin film devices of these compounds.     

High-spin molecules with magnetic anisotropy toward single-molecule magnets

High-spin molecules with easy-axis magnetic anisotropy show slow magnetic relaxation of spin-flipping along the axis of magnetic anisotropy and are called single-molecule magnets (SMMs). SMMs behave as molecular-size permanent magnets at low temperature and magnetic relaxation occurs by quantum tunneling processes; such molecules are promising candidates for use in quantum devices. We first discuss intramolecular ferromagnetic interactions for preparing high-spin molecules. Second, we determine the magnetic anisotropy for single metal ions with d(n) configurations and discuss how molecular anisotropy arises from single-ion anisotropy of the assembled component metal ions.     

Charging of metal clusters in helium droplets exposed to intense femtosecond laser pulses

We review the strong field (10(13)-10(16) W cm(-2)) laser excitation of metal clusters (Cd(N), Ag(N) and Pb(N)) embedded in He nanodroplets. Plasmon enhanced ionization obtained by stretching the laser pulses to several hundreds of femtoseconds or by using dual pulses with a suitable optical delay leads to a Coulomb explosion of highly charged atomic ions. The charging dynamics can be well described by corresponding semiclassical Vlasov simulations. The influence of the He environment on the ionization process and on the final charge distribution is discussed. Evidence is found that He(2+) is generated in collisions with highly charged metal ions. In contrast, singly and doubly charged ions with low recoil energies induce the formation of He snowballs with a distinct shell structure around the ion. Laser intensity thresholds for snowball formation and for the ionization of clusters are investigated by applying intensity selective scanning.     

Simulation of environmental effects on coherent quantum dynamics in many-body systems

In this paper we describe an application of the trajectory-based semiclassical Liouville method for modeling coherent molecular dynamics on multiple electronic surfaces to the treatment of the evolution and decay of quantum electronic coherence in many-body systems. We consider a model representing the coherent evolution of quantum wave packets on two excited electronic surfaces of a diatomic molecule in the gas phase and in rare gas solvent environments, ranging from small clusters to a cryogenic solid. For the gas phase system, the semiclassical trajectory method is shown to reproduce the evolution of the electronic-nuclear coherence nearly quantitatively. The dynamics of decoherence are then investigated for the solvated systems using the semiclassical approach. It is found that, although solvation in general leads to more rapid and extensive loss of quantum coherence, the details of the coupled system-bath dynamics are important, and in some cases the environment can preserve or even enhance quantum coherence beyond that seen in the isolated system.     

Plasmonic giant quantum dots: hybrid nanostructures for truly simultaneous optical imaging,photothermal effect and thermometry

Hybrid semiconductor–metal nanoscale constructs are of both fundamental and practical interest. Semiconductor nanocrystals are active emitters of photons when stimulated optically, while the interaction of light with nanosized metal objects results in scattering and ohmic damping due to absorption. In a combined structure, the properties of both components can be realized together. At the same time, metal–semiconductor coupling may intervene to modify absorption and/or emission processes taking place in the semiconductor, resulting in a range of effects from photoluminescence quenching to enhancement. We show here that photostable ‘giant’ quantum dots when placed at the center of an ultrathin gold shell retain their key optical property of bright and blinking-free photoluminescence, while the metal shell imparts efficient photothermal transduction. The latter is despite the highly compact total particle size (40–60 nm “inorganic” diameter and <100 nm hydrodynamic diameter) and the very thin nature of the optically transparent Au shell. Importantly, the sensitivity of the quantum dot emission to local temperature provides a novel internal thermometer for recording temperature during infrared irradiation-induced photothermal heating.     

Structural evolution of subnano platinum clusters

We present a theoretical study of the structural evolution of small minimum energy platinum clusters, using density functional theory (DFT). Three growth pathways were identified. At the subnanoscale, clusters with triangular packing are energetically most favorable. At a cluster size of approximately n = 19, a structural transition from triangular clusters to icosahedral clusters occurs. A less energetically favorable transition from triangular clusters to fcc‐like clusters takes place at around n = 38. Ionization potentials, electron affinities, and magnetic moments of the triangular clusters were also calculated. Understanding the structures and properties will facilitate studies of the chemical reactivity of Pt nanoclusters toward small molecules. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Physical properties of high-nuclearity metal cluster compounds

Metal cluster compounds are composed of large macromolecules, which consist of a metal core (cluster) containing a certain number (n=6–560) of metal atoms, to which core a shell of ligands is coordinated. They provide excellent model systems for an assembly of identical metal clusters, embedded in a dielectric matrix. We discuss a number of physical properties of these materials.     

Semiclassical quantum unimolecular reaction rate theory revisited

We describe a semiclassical quantum unimolecular reaction rate theory derived from the corresponding classical theory developed by Davis, Gray, Rice and Zhao (DGRZ). The analysis retains the intuitively useful mechanistic distinctions between intramolecular energy transfer and reaction, with the consequence that the semiclassical quantum theory version neglects some interference effects in the reaction dynamics. In the limiting case that intramolecular energy transfer is very fast compared to the rate of reaction we show that the DGRZ representation of the rate constant can be transformed, using the Weyl correspondence between quantum operators and classical variables, to the quantum flux–flux correlation function representation of the rate constant. In the more general case that the rate of intramolecular energy transfer influences the reaction dynamics, the semiclassical representation of the Wigner function for a classical system with both quasiperiodic and chaotic motion is used to obtain the reaction rate constant. Our analysis identifies the quantum analogue of the classical bottleneck to intramolecular energy transfer with the scars of unstable periodic orbits; it leads to a flux–flux correlation function representation of the rate constant for intramolecular energy transfer.